Integral Bounds Determination in Spherical Coordinates

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SUMMARY

The discussion focuses on determining the integral bounds of the angle phi (φ) in spherical polar coordinates for a specific problem. The user has attempted to set φ to π/4 based on graphical analysis but seeks validation and proof of this choice. The conversation emphasizes the importance of understanding the geometric interpretation of spherical coordinates to accurately establish these bounds.

PREREQUISITES
  • Spherical coordinates and their applications
  • Understanding of integral calculus
  • Graphical interpretation of three-dimensional shapes
  • Familiarity with polar coordinate transformations
NEXT STEPS
  • Study the geometric interpretation of spherical coordinates
  • Learn about integral bounds in multiple dimensions
  • Explore examples of integral calculations in spherical coordinates
  • Review the properties of angles in three-dimensional space
USEFUL FOR

Students in calculus, mathematicians working with three-dimensional integrals, and anyone studying spherical coordinates in physics or engineering.

DHB_Integral
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Homework Statement



How to determine the integral bounds of phi in spherical polar coordinates. Please see my exact question at the end of page 2 of 2 in attachments.

Homework Equations



Please see my attachments

The Attempt at a Solution


Please see my attachments.
 

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Last edited:
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I just tried out the integral bounds of phi , it can work getting the correct result. but It cannot convince myself in terms of the bounds of phi, based on the graph on page 1, it should be equal to pi/4. So, how to prove the bounds of phi? Please help with question.

Thanks a lot in advance.
 
Last edited:

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